Technical Abstract:
A two-step analysis is proposed in which test day effects are estimated within herd with adjustment for across-herd effects, and then the adjusted data are analyzed across herd. Genetic effects are defined for each of 10 mo in milk within first and later lactation and for milk, fat and protein for a total of 60 traits. The rank of the genetic (co)variance matrix (G) is reduced to 6 such that G spans the space defined by six linear combinations: the sum for milk, fat, and protein each; linear and quadratic functions of months in milk; and difference between first and later yields. A repeatability model allows for multiple lactations with each lactation conceptually expressing all 60 traits but with missing observations for 30 or more traits. A canonical transformation is applied to create uncorrelated traits. Missing values are replaced by their expectations at each round. Because of the rank reduction, only six canonical traits are solved for. Periodically, the solutions are backtransformed and used in the first step. This system should make evaluations more stable by removing biases due to genetic differences in persistency and rate of maturity.